Derivative wrt one variable of an integral wrt another

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  • #1
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I can't seem to find this anywhere. What's
d/dn(∫ n(w) dw)?

That's the derivative wrt n of the integral of n over w (note: n is a function of w). Seems straightforward enough. Is there a simplification?

Thanks
 

Answers and Replies

  • #2
mathman
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The notation you are using to express what you want is confusing. Under the integral sign, n is a function. Outside it is a variable.
 
  • #3
HallsofIvy
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But a function is a variable! One can always define the derivative of y with respect to a function, f(x)- dy/dx= (dy/df)(df/dx) so dy/df= (dy/dx)/(df/dx).

So [itex]d/df \int f(x)dx= (d(\int f(x)dx)/dx)(df/dx)= f(x)(dy/dx)[/itex].
 
  • #4
mathman
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But a function is a variable! One can always define the derivative of y with respect to a function, f(x)- dy/dx= (dy/df)(df/dx) so dy/df= (dy/dx)/(df/dx).

So [itex]d/df \int f(x)dx= (d(\int f(x)dx)/dx)(df/dx)= f(x)(dy/dx)[/itex].
Where did y come from?
 

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